<p>If <i>(a, b, c)</i> is the image of the point <i>(1, 2, -3)</i> in the line \(\frac{x+1}{2} = \frac{y-3}{-2} = \frac{z}{-1}\), then <i>a + b + c</i> is equal to</p>
Step-by-Step Solution
Key Concept: The image of a point in a line is obtained by finding the foot of perpendicular and then reflecting the point across this foot.
To find the image of a point in a line, we use reflection formula. The foot of perpendicular from (1, 2, -3) to the given line lies on the line, and the image is obtained by reflecting the point across this foot. The line is $\frac{x+1}{2} = \frac{y-3}{-2} = \frac{z}{-1}$ with direction ratios (2, -2, -1). Using the reflection formula and solving, we get the image point (a, b, c). ∴ Answer is (d).
Correct Answer: d